Deck 16: Simulation Models

Question 1

In a manufacturing model,we might simulate the number of days to produce a batch and the yield from each batch.The number of days would typically be a ___________ distribution and the yield would be a ___________ distribution.

A)Continuous,discrete
B)Continuous,continuous
C)Discrete,continuous
D)Discrete,discrete

Answer 1

C

Question 2

Which of the following is among the questions that financial analysts try to answer with simulation models?

A)Mean and variance of a project NPV
B)Probability that a project with have a negative NPV
C)Probability that a company will have to borrow a certain amount during the next year
D)Mean and variance of a company's profit during the next fiscal year
E)All of these options

Answer 2

E

Question 3

Suppose we have a 0-1 output for whether a bidder wins a contract in a bidding model (0=bidder does not win contract,and 1=bidder wins contract).From the mean of this output we can tell:

A)the number of times the bidder wins the contract
B)the number of times the bidder does not win the contract
C)the probability that the bidder will win the contract
D)the probability that the bidder will not win the contract
E)None of these options

Answer 3

C

Question 4

Customer loyalty models are an example of which of the following types of simulation application?

A)Operations models
B)Financial models
C)Marketing models
D)Games of chance
E)None of these options

Question 5

Bidding for contracts is an example of which of the following types of simulation model application?

A)Operations models
B)Financial models
C)Marketing models
D)Games of chance
E)None of these options

Question 6

Which of the following distributions is most likely to be used to develop a simulation model for estimating the time until failure of a product in a simulation model?

A)Binomial
B)Gamma
C)Normal
D)Chi-square

Question 7

Suppose we compare the difference between the NPV of a financial model in which the means are entered for all input random variables and the NPV of a financial model in which the most likely values are entered for all input random variables.If we see a large difference between the NPV's,this illustrates:

A)the value at risk (VAR)
B)the effect of randomness
C)the flaw of averages
D)the bias of the analyst
E)None of these options

Question 8

Which of the following is typically not an application of simulation models?

A)Operations models
B)Financial models
C)Marketing models
D)Value of Information models
E)None of these options

Question 9

Which of the following functions is not an @RISK statistical function?

A)RISKMIN
B)RISKMAX
C)RISKPERCENTILE
D)RISKSIMTABLE
E)None of these options

Question 10

In cash flow models,we are typically interested in investigating:

A)the value at risk (VAR)
B)the net present value (NPV)
C)the amount of loans required to maintain a minimum cash balance
D)the interest on loans taken out by a firm
E)None of these options

Question 11

The value at risk (VAR)is typically defined as the:

A)5^th percentile of NPV distribution
B)10^th percentile of NPV distribution
C)50^th percentile of NPV distribution
D)90^th percentile of NPV distribution
E)95^th percentile of NPV distribution

Question 12

Financial analysts often investigate the value at risk (VAR)with simulation models.VAR is an indicator of:

A)how much to bid for a project
B)the expected amount of loss for a project
C)what is nearly the worst possible outcome for a project
D)the required amount of investment required for a project
E)None of these options

Question 13

Which of the following functions is often required in simulations where we must model a process over multiple time periods and must deal with uncertain timing of events?

A)RISKMIN
B)RISKMAX
C)NPV
D)IF
E)None of these options

Question 14

Which of the following is not among the financial applications where simulation can be applied?

A)Future stock prices
B)Customer preferences for different attributes of products
C)Future interest rates
D)Future cash flows
E)None of these options

Question 15

Cash balance models are an example of which of the following types of simulation application?

A)Operations models
B)Financial models
C)Marketing models
D)Games of chance
E)None of these options

Question 16

Which of the following functions is not appropriate in cases where we run a single simulation?

A)RISKMIN
B)RISKMAX
C)RISKPERCENTILE
D)RISKSIMTABLE
E)None of these options

Question 17

Which of the following @RISK functions can be used to find the probability of a particular value in an output distribution?

A)RISKMIN
B)RISKMAX
C)RISKPERCENTILE
D)RISKTARGET
E)None of these options

Question 18

The amount of variability of a financial output caused by different inputs can be investigated using:

A)the NPV function
B)a histogram of the NPV
C)a tornado chart of NPV
D)the value at risk (VAR)
E)All of these options

Question 19

In a warranty cost modeling model,which of the following is a key input random variable?

A)Warranty cost
B)Warranty time limitation
C)Lifetime of product
D)Replacement cost of product
E)All of these options

Question 20

The two random variables we typically simulate as inputs in bidding models are?

A)Number of bidding competitors and bid amount
B)Number of bidding competitors and bid profit
C)Individual bid amounts and net bidding profits
D)Mean number of bidding competitors and net bidding profit
E)None of these options

Question 21

Which of the following are not among the marketing applications of simulation?

A)The entry of new brands into the market
B)Customer preferences for different attributes of products
C)Brand-switching behavior of customers
D)The effect of advertising on sales
E)None of these options

Question 22

The main issue in marketing and sales models is:

A)the amount invested in marketing
B)the timing of marketing
C)the profit from sales
D)the timing of sales
E)the tradeoff between marketing and sales

Question 23

We can use the RISKSIMTABLE function to summarize the results of a single simulation of product lifetime.

Question 24

Uncertain timing and the events that follow in process modeling can be modeled using IF statements.

Question 25

Using @RISK summary functions such as RISKMEAN,RISKPERCENTILE,and others allows us to capture simulation results in the same worksheet as the simulation model.

Question 26

Although we can determine the optimal bid and the expected profit from that bid in a bidding simulation,we usually cannot determine the probability of winning.

Question 27

A common distribution for modeling product lifetimes is the binomial distribution

Question 28

We can use Excel's RAND function inside an IF function to simulate whether some event occurs or does not occur.

Question 29

In a manufacturing setting,a discrete distribution is natural for modeling the number of days to produce a batch,and a continuous distribution is appropriate for modeling the yield from a batch.

Question 30

RISKTARGET is a function that allows us to determine the cumulative probability of a particular value in an output distribution,such as the probability of meeting a due date in manufacturing.

Question 31

In warranty cost models,the key input random variable is product lifetime.

Question 32

The primary objective in simulation models of bidding for contracts is to determine the optimal bid.

Question 33

In investment models,a useful approach for generating future returns and inflation factors from historical data is:

A)the NPV approach
B)the scenario approach
C)the averaging approach
D)the trend analysis approach
E)None of these options

Question 34

In a bidding model,once we have the bidding strategy that maximizes the expected profit,we no longer should consider the bidders risk aversion.

Question 35

A key input variable in many marketing models of customer loyalty is the:

A)Mean profit per customer
B)Number of customers
C)Churn rate
D)Time horizon
E)All of these options

Question 36

Simulation applications involving games of chance are primarily for learning the background of simulation (e.g.,modeling gambling casinos of Monte Carlo),since they are not business applications per se.

Question 37

In bidding models,the simulation input variable is the number of competitors who will bid.

Question 38

RISKMAX and RISKMIN are can be used to find the probability of meeting a given due date in a manufacturing model.

Question 39

Churn is an example of the type of uncertain variable we deal with in financial models.

Question 40

In a marketing and sales model,which of the following might be a good choice for a discrete distribution to model the random timing of sales?

A)RAND()
B)Normal distribution
C)Binomial distribution
D)Exponential distribution
E)Poisson distribution

Question 41

What does the distribution of the NPV look like?

Question 42

In marketing and sales models,the primary issue is the uncertain amount of sales that can be obtained,given an assumed timing.

Question 43

The Net Present Value (NPV)is the sum of the discounted cash flows.What is the NPV of the project,including the required investment?

Question 44

What is the probability that Amanda will have less than $500,000 in her retirement account after 30 years?

Question 45

What is the standard deviation of the ending balance? What does the distribution look like? What should Amanda infer from this?

Question 46

In marketing models of customer loyalty,we are typically interested in modeling the rate of customer retention,called churn.

Question 47

A key objective in cash flow models is often to determine the amount of debt that must be taken out to maintain a minimum cash balance.

Question 48

Suppose that the forecasted price levels shown in the pro forma cash flow sheet are not deterministic,but rather are expected to fluctuate due to market forces.The prices are expected to be normally distributed in each year,with the means equal to the expected values shown in the pro forma,but with standard deviations of $5.2,$5.3,and $5.5 in years 1,2,and 3,respectively.Enter this pro forma in an Excel worksheet,with the appropriate @RISK functions for the random prices,and simulate 1,000 iterations.What is the expected NPV now? Would you recommend investing in this project? Explain.

Question 49

The @RISK function RISKDUNIFORM in the form = RISKDUNIFORM ({List})generates a random member of a given list,so that each member of the list has the same chance of being chosen.

Question 50

What is the standard deviation of the NPV? What does it indicate?

Question 51

What are the chances the firm could loose money on this project,given the price uncertainty?

Question 52

In financial simulation models,we are typically more interested in the expected NPV of a project than in the extremes of the outcomes.

Question 53

In investment models,we typically must simulate the random investment weights

Question 54

A marketing simulation model can be used to determine the expected profit under uncertain customer loyalty,and then we can use an optimization model to determine the optimal amount to spend on increasing customer loyalty.

Question 55

Suppose Amanda will stop investing in the stock market and transfer all of her retirement into a savings account if and when she reaches $500,000.When can she expect to reach this goal?

Question 56

In financial simulation models,the value at risk (VAR)is the 5^th percentile of an output distribution,and it indicates nearly the worst possible outcome.

Question 57

A tornado chart lets us see which random input has the most effect on a specified output in a financial model.

Question 58

A @RISK output range allows us to obtain a summary chart that shows the entire simulated range at once.

Question 59

Given your answers to Questions 51 through 55,would you invest in this project?

Question 60

Simulate Amanda's portfolio over the next 30 years and determine how much she can expect to have in her account at the end of that period.At the beginning of each year,compute the beginning balance in Amanda's account.Note that this balance is either 0 (for year 1)or equal to the ending balance of the previous year.The contribution of $5,000 is then added to calculate the new balance.The market return for each year is given by a normal random variable with the parameters above (assume the market returns in each year are independent of the other years).The ending balance for the each year is then equal to the beginning balance,augmented by the contribution,and multiplied by (1+Market return).

Question 61

What is the standard deviation of the ending balance? What does the distribution look like now? What should Amanda infer from this?

Question 62

Suppose again that Amanda will stop investing in the stock market and transfer all of her retirement into a savings account if and when she reaches $500,000.When can she expect to reach this goal under the more conservative investing strategy?

Question 63

Suppose a 1% increase in market share is worth $10,000 per week to company A.Company A believes that for a cost of $1 million per year it can cut the percentage of unsatisfactory juice cartons in half.Is this worthwhile? (Use the same values of , ,and as in Question 66.

Question 64

Next,assume that one of the bidders bids 20% below his or her estimated value,while the other two bidders follow the same strategy as in Question 74.Using 1000 iterations report the expected profit or loss to the conservative bidder.

Question 65

What is the probability that Amanda will have less than $500,000 in her retirement account after 30 years under the more conservative investing strategy?

Question 66

Suppose first that all three bidders are aware of the winner's curse so they have decided (independently)to bid 10% below their estimated values.Using 1000 iterations report the expected profit (or loss)to the winner.

Question 67

Which simulation yields the largest median NPV?

Question 68

What if the GM satisfaction rate is raised further to 90%.What would the customer NPV be in that case?

Question 69

Does the answer to Question 72 match your intuition? Explain why or why not.

Question 70

Suppose GM could raise it customer satisfaction to 85%,to match Toyota's.What would the customer NPV be in that case?

Question 71

Perform a simulation assuming the plant will be designed to meet the expected demand.What is the NPV in that case?

Question 72

Using your answers to Questions 69 and 70,and without simulating the model again,estimate how much an extra 5% customer satisfaction is worth to GM.

Question 73

Next,suppose Amanda's broker thinks the stock market may be too risky and has advised her to diversity by investing some of her money in money market funds and bonds.He estimates that this will lower her expected annual return to 10% per year,but will also lower the standard deviation to 10%.What can she expect to have in her account after thirty years under this investing strategy?

Question 74

After a year,what will the market share for each of the three companies be? Assume = 0.10, = 0.15,and = 0.20.(Hint: Use the RISKBINOMIAL function to model how many people switch from A,then how many switch from A to B and from A to C.)

Question 75

Consider a customer whose first car is GM.If profits are discounted at 10% annually,use simulation to estimate the value of this customer to GM over the customer's lifetime.

Question 76

What is the probability of winning for the conservative bidder?

Question 77

Suppose that Coke and Pepsi are fighting for the cola market.Each week each person in the market buys one case of Coke or Pepsi.If the person's last purchase was Coke,there is a 0.80 probability that this person's next purchase will be Coke; otherwise,it will be Pepsi.(We are considering only two brands in the market.)Similarly,if the person's last purchase was Pepsi,there is a 0.90 probability that this person's next purchase will be Pepsi; otherwise,it will be Coke.Currently half of all people purchase Coke,and the other half purchase Pepsi.Simulate one year of sales in the cola market and estimate each company's average weekly market share.Do this by assuming that the total market size is fixed at 100 customers.(Hint: Use the RISKBINOMIAL function.)

Question 78

What is the probability of winning for each bidder in the above scenario?

Question 79

Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be.

Question 80

Suppose that a customer satisfaction firm approaches GM with a proposal to increase satisfaction from the current 80% rate to $85% through a low cost maintenance program that will cost GM $300 per customer.Would the program be worth it?